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We analyze the volume-limited nearly complete 100 pc sample of 95 halo whitedwarf candidates identified by the second data release of Gaia. Based on adetailed population synthesis model, we apply a method that relies on Gaiaastrometry and photometry to accurately derive the individual white dwarfparameters (mass, radius, effective temperature, bolometric luminosity andage). This method is tested with 25 white dwarfs of our sample for which wetook optical spectra and performed spectroscopic analysis. We build and analysethe halo white dwarf luminosity function, for which we find for the first timepossible evidences of the cut-off at its faintest end, leading to an ageestimate of $\simeq12\pm0.5 $Gyr. The mass distribution of the sample peaks at$0.589\,M_{\odot}$, with $71\%$ of the white dwarf masses below$0.6\,M_{\odot}$ and just two massive white dwarfs of more than$0.8\,M_{\odot}$. From the age distribution we find three white dwarfs withtotal ages above 12 Gyr, of which J1312-4728 is the oldest white dwarf knownwith an age of $12.41\pm0.22 $Gyr. We prove that the star formation history ismainly characterised by a burst of star formation that occurred from 10 to 12Gyr in the past, but extended up to 8 Gyr. We also find that the peak of thestar formation history is centered at around 11 Gyr, which is compatible withthe current age of the Gaia-Enceladus encounter. Finally, $13\%$ of our halosample is contaminated by high-speed young objects (total age<7 Gyr). Theorigin of these white dwarfs is unclear but their age distribution may becompatible with the encounter with the Sagittarius galaxy.

The Gaia DR2 halo white dwarf population: the luminosity function, mass distribution and its star formation history